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(a) Obtain the general solution of the differential equation. (b) Impose the initial conditions to obtain the unique solution of the init ial value problem. (c) Describe the behavior of the solution as t → -o and t → 0o. In each case, does y(t) approach -o, +0, or a finite limit? 1. y" + 2y' + y = 0, y(1) = 1, y'(1) = 0 2. 9y" – 6y' + y = 0, y(3) = -2, y (3) = - 3. y" + 6y' + 9y = 0, y(0) = 2. y'(0) = -2 4. 25y" + 20y' + 4y = 0, y(5) = 4e-, y'(5) = -je-2 5. 4y" – 4y' + y = 0, y(1) = -4. y(1) = 0 6. у" - 4y + 4y %3 0, у(-1) %3D2. у (-1) %3D 1 7. 16y" – 8y' + y = 0, y(0) = -4, y'(0) = 3

(a) Obtain the general solution of the differential equation. (b) Impose the initial conditions to obtain the unique solution of the init ial value problem. (c) Describe the behavior of the solution as t → -o and t → 0o. In each case, does y(t) approach -o, +0, or a finite limit? 1. y" + 2y' + y = 0, y(1) = 1, y'(1) = 0 2. 9y" – 6y' + y = 0, y(3) = -2, y (3) = - 3. y" + 6y' + 9y = 0, y(0) = 2. y'(0) = -2 4. 25y" + 20y' + 4y = 0, y(5) = 4e-, y'(5) = -je-2 5. 4y" – 4y' + y = 0, y(1) = -4. y(1) = 0 6. у" - 4y + 4y %3 0, у(-1) %3D2. у (-1) %3D 1 7. 16y" – 8y' + y = 0, y(0) = -4, y'(0) = 3

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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section 3.4

Exercises 1-9: (a) Obtain the general solution of the differential equation. (b) Impose the initial conditions to obtain the unique solution of the initial value problem. (c) Describe the behavior of the solution as t → -o and t → o. In each case, does y(t) approach -o, +00, or a finite limit? 1. y" + 2y' + y = 0, y(1) = 1, y(1) = 0 2. 9y" – 6y' + y = 0, y(3) = -2, y (3) = - 3. y" + 6y' + 9y = 0, y(0) = 2. y' (0) = -2 4. 25y" + 20y' + 4y = 0, y(5) = 4e-2, y'(5) = -je-2 5. 4y" – 4y' + y = 0, y(1) = -4, y(1) = 0 6. y" – 4y' + 4y = 0, y(-1) = 2, y'(-1) = 1 7. 16y" – 8y' + y = 0, y(0) = -4, y'(0) = 3
Transcribed Image Text:Exercises 1-9: (a) Obtain the general solution of the differential equation. (b) Impose the initial conditions to obtain the unique solution of the initial value problem. (c) Describe the behavior of the solution as t → -o and t → o. In each case, does y(t) approach -o, +00, or a finite limit? 1. y" + 2y' + y = 0, y(1) = 1, y(1) = 0 2. 9y" – 6y' + y = 0, y(3) = -2, y (3) = - 3. y" + 6y' + 9y = 0, y(0) = 2. y' (0) = -2 4. 25y" + 20y' + 4y = 0, y(5) = 4e-2, y'(5) = -je-2 5. 4y" – 4y' + y = 0, y(1) = -4, y(1) = 0 6. y" – 4y' + 4y = 0, y(-1) = 2, y'(-1) = 1 7. 16y" – 8y' + y = 0, y(0) = -4, y'(0) = 3
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